In menopause, in the absence of estrogen, the vagina narrows and becomes more thin and fragile. Even when you are lubricated enough, the tissues have likely lost elasticity and can’t comfortably stretch with intercourse. Some light bleeding represents the "trauma" to those tissues and usually comes from near the opening of the vagina or the vaginal tissues themselves.

Using a vaginal moisturizer (like Yes, Replens, or KY Luiqibeads) would almost certainly help. It may also beneficial to use dilators to try to get back more caliber or capacity (dilators literally stretch the tissues gradually). You might also talk to your health care provider about vaginal estrogen, also known as localized estrogen, which may be of benefit to you in restoring elasticity.